A particle of mass m = 3 kg has position vector r(t) = [t2 i + t(1+t)j + 2t2 k] m. Find the velocity and acceleration vector of the particle at t=1.

April 27, 2026Physics

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April 27, 2026

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3 , \text{kg}$

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Given: Mass $m = 3 \, \text{kg}$ Position vector $\vec{r}(t) = [t^2 \hat{i} + t(1+t)\hat{j} + 2t^2 \hat{k}] \, \text{m}$ This can be written as $\vec{r}(t) = [t^2 \hat{i} + (t+t^2)\hat{j} + 2t^2 \hat{k}] \, \text{m}$ .

a) The velocity and acceleration vector of the particle at $t=1$

Step 1: Find the velocity vector $\vec{v}(t)$ by differentiating

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Here's the solution to your problem. Given: Mass m = 3 \, kg Position vector r(t) = [t^2 i + t(1+t)j + 2t^2 k] \, m This can be written as r(t) = [t^2 i + (t+t^2)j + 2t^2 k] \, m.

Asked on April 27, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI AnswerAnswered on April 27, 2026

Here's the solution to your problem. Given: Mass m = 3 \, kg Position vector r(t) = [t^2 i + t(1+t)j + 2t^2 k] \, m This can be written as r(t) = [t^2 i + (t+t^2)j + 2t^2 k] \, m. a) The velocity and acceleration vector of the particle at t=1 Step 1: Find the velocity vector v(t) by differentiating